M7MBA wrote:What is the difference between the fourth and third terms of the sequence defined by \(a_n=3^n−n^2?\)

A) 18

B) 23

C) 47

D) 65

E) 83

[spoiler]OA=C[/spoiler]

Source: Magoosh

\(a_4=3^4−4^2 = 81-16=65\);
\(a_3=3^3−3^2=27-9=18\);

Thus, the difference between the fourth and third terms = 65 - 18 = 47

The correct answer: C

Hope this helps!

-Jay
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M7MBA wrote:What is the difference between the fourth and third terms of the sequence defined by \(a_n=3^n−n^2?\)

A) 18

B) 23

C) 47

D) 65

E) 83

[spoiler]OA=C[/spoiler]

Source: Magoosh

The difference is:

(3^4 - 4^2) - (3^3 - 3^2)

81 - 16 - 27 + 9 = 90 - 43 = 47

Answer: C

Hi All,

We're asked for the difference between the fourth and third terms of the sequence defined by 3^N - N^2. Most sequence questions can be solved with a bit of 'brute force' - simply calculate the individual terms and you'll have the answer without too much trouble.

Based on the specific sequence defined in this question, the first several terms would be:

1st = 3^1 - 1^2 = 3 - 1 = 2
2nd = 3^2 - 2^2 = 9 - 4 = 5
3rd = 3^3 - 3^2 = 27 - 9 = 18
4th = 3^4 - 4^2 = 81 - 16 = 65

The difference between the 4th and 3rd terms is 65 - 18 = 47

Final Answer: C

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